The field of the invention is nuclear magnetic resonance imaging methods and systems. More particularly, the invention relates to methods for acquiring magnetic resonance imaging (“MRI”) data using a sensitivity encoding (“SENSE”) technique.
When a substance such as human tissue is subjected to a uniform magnetic field (polarizing field B0), the individual magnetic moments of the spins in the tissue attempt to align with this polarizing field, but precess about it in random order at their characteristic Larmor frequency. If the substance, or tissue, is subjected to a magnetic field (excitation field B1) which is in the x-y plane and which is near the Larmor frequency, the net aligned moment, Mz, may be rotated, or “tipped”, into the x-y plane to produce a net transverse magnetic moment Mt. A signal is emitted by the excited spins after the excitation signal B1 is terminated, this signal may be received and processed to form an image.
When utilizing these signals to produce images, magnetic field gradients (Gx Gy and Gz) are employed. Typically, the region to be imaged is scanned by a sequence of measurement cycles in which these gradients vary according to the particular localization method being used. The resulting set of received NMR signals are digitized and processed to reconstruct the image using one of many well known reconstruction techniques.
The present invention will be described with reference to a variant of the well known Fourier transform (FT) imaging technique, which is frequently referred to as “spin-warp”. The spin-warp technique is discussed in an article entitled “Spin-Warp NMR Imaging and Applications to Human Whole-Body Imaging” by W. A. Edelstein et al., Physics in Medicine and Biology, Vol. 25, pp. 751–756 (1980). It employs a variable amplitude phase encoding magnetic field gradient pulse prior to the acquisition of NMR spin-echo signals to phase encode spatial information in the direction of this gradient. In a two-dimensional implementation (2DFT), for example, spatial information is encoded in one direction by applying a phase encoding gradient (Gy) along that direction, and then a spin-echo signal is acquired in the presence of a readout magnetic field gradient (Gx) in a direction orthogonal to the phase encoding direction. The readout gradient present during the spin-echo acquisition encodes spatial information in the orthogonal direction. In a typical 2DFT image acquisition, a series of pulse sequences is performed in which the magnitude of the phase encoding gradient pulse Gy in the pulse sequence is incremented (ΔGy). The resulting series of views that is acquired during the scan form an NMR image data set from which an image can be reconstructed. The acquisition of each phase encoded view requires a finite amount of time, and the more views that are required to obtain an image of the prescribed field of view and spatial resolution, the longer the total scan time.
Reducing scan time is a very important objective in MRI. In addition to improved patient comfort, shorter scan times free up the imaging system for more patients and reduces image artifacts caused by patient motion. SENSE (SENSitivity Encoding) is a technique described by K. P. Pruessmann, et al., “SENSE: Sensitivity Encoding for Fast MRI”, J. Magn. Reson. 42, 952–962 (1999), which reduces MRI data acquisition time by using multiple local coils. The idea is to reduce acquisition time by increasing the step size (ΔGy) between phase encoding views, or equivalently, by reducing the field of view. In either case, the total number of views is reduced with a consequent reduction in scan time. If the object extends outside the reduced field of view, however, aliasing or wrap-around occurs in the phase encoding direction. The SENSE technique removes this aliasing by using knowledge of the surface coil receive field (also called sensitivities) to find the unaliased spin distribution.
For simplicity, one can consider the image intensity variation only in the phase encoding direction, which may be, for example, the y direction. N local coils with B1 receive field sensitivities Sj(y) where j=0, 1, . . . N−1 are used to acquire the NMR data. The reconstructed image intensity for each local coil is weighted by its receive field. If the reconstructed image for coil j is lj(y), and the ideal proton density distribution, including T1 and T2 weighting factors, is M(y), thenIj(y)=Sj(y)M(y).  (1)
Aliasing or replication occurs in an MR image in the phase encode direction. The replication distance is the same as the field of view. If the field of view FOV is chosen such that the subject is completely contained within this field of view, the replicates of the subject do not overlap and no artifact results in the reconstructed image. If the field of view is reduced in the y direction by a factor of R, the scan time is also correspondingly reduced by a factor of R. However, now the reconstructed image is aliased or replicated in the y direction at multiples of FOV/R=D and aliasing replicates now overlap with resulting loss of diagnostic utility. Mathematically, the image intensity is nowIj(y)=Sj(y)M(y)+Sj(y+Δy)M(y+Δy)+ . . . +Sj(y+(A−1)Δy)M(y+(A−1)Δy),for 0≦yΔy. Or, the image intensity may be expressed as:
                                          I            j                    ⁡                      (            y            )                          =                              ∑                          k              =              0                                      A              -              1                                ⁢                                                    S                j                            ⁡                              (                                  y                  +                  kD                                )                                      ⁢                          M              ⁡                              (                                  y                  +                  kD                                )                                                                        (        2        )            where j refers to coil number, sj(y) is the sensitivity of coil j, m(y) is the spin density (including relaxation effects), D is the reduced phase encoding FOV (i.e., D is the original FOV divided by R) and A is the number of aliased replicates at the pixel. If the local coil sensitivities Sj(y) are known, and if N≧R, the proton distribution M(y) can be obtained by solving the resulting N equations. In matrix form equation (2) can be writtenI=SM,  (3)where:
                              I          =                      [                                                                                                      I                      0                                        ⁡                                          (                      y                      )                                                                                                                                                              I                      1                                        ⁡                                          (                      y                      )                                                                                                                    ⋮                                                                                                                        I                                              N                        -                        1                                                              ⁡                                          (                      y                      )                                                                                            ]                          ,                            (        4        )                                          M          =                      [                                                                                M                    ⁡                                          (                      y                      )                                                                                                                                        M                    ⁡                                          (                                              y                        +                        D                                            )                                                                                                                    ⋮                                                                                                  M                    (                                          y                      +                                                                        (                                                      A                            -                            1                                                    )                                                ⁢                        D                                                                                                                  ]                          ,                                  ⁢        and                            (        5        )                                S        =                              [                                                                                                      S                      0                                        ⁡                                          (                      y                      )                                                                                                                                                          S                        0                                            ⁡                                              (                                                  y                          +                          D                                                )                                                              ⁢                                                                                  ⁢                    …                    ⁢                                                                                  ⁢                                                                  S                        0                                            ⁡                                              (                                                  y                          +                                                                                    (                                                              A                                -                                1                                                            )                                                        ⁢                            D                                                                          )                                                                                                                                                                                    S                      1                                        ⁡                                          (                      y                      )                                                                                                                                                          S                        1                                            ⁡                                              (                                                  y                          +                          D                                                )                                                              ⁢                                                                                  ⁢                    …                    ⁢                                                                                  ⁢                                                                  S                        1                                            ⁡                                              (                                                  y                          +                                                                                    (                                                              A                                -                                1                                                            )                                                        ⁢                            D                                                                          )                                                                                                                                          ⋮                                                                                                                                                                                                                S                                              N                        -                        1                                                              ⁡                                          (                      y                      )                                                                                                                                                          S                                                  N                          -                          1                                                                    ⁡                                              (                                                  y                          +                          D                                                )                                                              ⁢                                                                                  ⁢                    …                    ⁢                                                                                  ⁢                                                                  S                                                  N                          -                          1                                                                    ⁡                                              (                                                  y                          +                                                                                    (                                                              A                                -                                1                                                            )                                                        ⁢                            D                                                                          )                                                                                                                  ]                    .                                    (        6        )            Note that I and M are N×1 and A×1 dimensional matrices, respectively, while S has dimensions N×A. The solution of equation (3) is efficiently determined using the pseudoinverse of S. Denoting the complex conjugate transpose of S as S* then{circumflex over (M)}=[(S*S)−1S*]I  (7)
Typically, the coil sensitivity values Sj(y) are obtained by performing two calibration scans. The calibration scans are performed with the subject of the scan in place and throughout the full prescribed field of view. Calibration data from one scan is acquired with the body RF coil which has a substantially homogeneous receive field, and data from the second calibration scan is acquired using each of the N local coils. The B1 field sensitivity of each local coil is obtained by taking the ratio of the complex calibration images acquired with the body coil and each of the surface coils. For example, if Ijcal(y) and Ibodycal(y) are the respective full field of view calibration images obtained with surface coil j and the calibration image acquired with the body coil, the sensitivity of the surface coil j is estimated as
                                          S            j                    ⁡                      (            y            )                          =                                                            I                j                                  ca                  ⁢                                                                          ⁢                  l                                            ⁡                              (                y                )                                                                    I                body                                  ca                  ⁢                                                                          ⁢                  l                                            ⁡                              (                y                )                                              .                                    (        8        )            Note that the complex magnetization term M(y) drops out of the ratio in equation (8) if the body coil and the surface coil scans are performed using the same scan prescription. In this case, the reconstructed images have the proton distribution weighted by the body coil B1 field which is normally very homogeneous over the field of view. The sensitivity calibration data may also be obtained using combined signals from the N surface coils as described in co-pending U.S. patent application Ser. No. 09/851,775 filed on May 9, 2001 and entitled “Calibration Method For Use With Sensitivity Encoding MRI Acquisition”.
With the SENSE technique it is important to determine the number of overlapped aliased replicates A at each pixel. In general, A is not equal to R if the object is not exactly the same size in the phase encoding direction as the fall SENSE unreduced field of view (DR). If A is overestimated, the image noise will be greater than if A is exact because the geometry factor g will be greater. If A is underestimate, aliasing will not be fully corrected at the pixel.